BadMedicine here's something for you to try along the same lines. We raised "silkies" a type of chicken which are very broody. Those hens will hatch any egg that you put under them. So what we have done in the past is take the eggs from the pigeons (they will lay again if you do) and put them under the hen. That way you can more than double your bird production in the same amount of time. Just keep taking the eggs away from the pigeons and putting them under the hen.